# How do you find #\lim _ { x \rightarrow - 14} \frac { 13- \sqrt { x ^ { 2} - 27} } { x + 14}#?

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Let us solve the Problem, using the following Standard Form :

We suppose,

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To find (\lim_{x \to -14} \frac{13 - \sqrt{x^2 - 27}}{x + 14}), we can rationalize the numerator by multiplying both the numerator and denominator by the conjugate of the numerator. The conjugate of (13 - \sqrt{x^2 - 27}) is (13 + \sqrt{x^2 - 27}).

After rationalizing, we simplify the expression and then substitute (x = -14) into the resulting expression to find the limit.

The result of this process is that the limit is (\frac{1}{14}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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